Answer:
[tex]AC=15.4[/tex]
Step-by-step explanation:
In relation to the angle [tex]\theta[/tex], we are given the triangle's opposite side and hypotenuse. Therefore, we need to use the sine function to determine the hypotenuse:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]sin30^\circ=\frac{7.7}{h}[/tex]
[tex]hsin30^\circ=7.7[/tex]
[tex]h=\frac{7.7}{sin30^\circ}[/tex]
[tex]h=15.4[/tex]
Alternatively, since this is a 30-60-90 triangle, you can just multiply the opposite side by 2 to get the hypotenuse. Therefore, [tex]h=7.7*2=15.4[/tex] as well.
